Space with Euler characteristic zero
This article defines a property of topological spaces that depends only on the homology of the topological space, viz it is completely determined by the homology groups. In particular, it is a homotopy-invariant property of topological spaces
View all homology-dependent properties of topological spaces OR view all homotopy-invariant properties of topological spaces OR view all properties of topological spaces
Definition
A topological space is said to have zero Euler characteristic if it has finitely generated homology, and its Euler characteristic is zero.
Relation with other properties
Stronger properties
- Compact connected Lie group (nontrivial): For full proof, refer: compact connected nontrivial Lie group implies zero Euler characteristic
- Odd-dimensional compact connected orientable manifold: For full proof, refer: Euler characteristic of odd-dimensional compact connected orientable manifold is zero